面外剪切下各向异性三相椭圆夹杂中均匀应力

论证了只要合适选择中间界面层的弹性常数, 各向异性线弹性固体在远场均匀反平面剪切应力作用下三相椭圆夹杂内椭圆上仍存在均匀应力场. 讨论了内外两椭圆除过其中心相同外无其它任何几何限制条件. 所给出的数值算例显示出该结论的正确性. 该方法为纤维增强复合材料的设计提供了一条新途径.     

A rigid line in a confocal elliptic inhomogeneity embedded in an infinite medium under antiplane shear

An effective method is developed and used to investigate the antiplane problem of a rigid line in a confocal elliptic inhomogeneity embedded in an infinite medium. The analytical solution is obtained. The proposed method is based upon the use of conformal mapping and the theorem of analytic continuation. Special solutions which are verified by comparison with existing ones are provided. Finally, the characteristics of stress singularity at the tip of the rigid line inhomogeneity are analyzed and the extension forces for the crack and the rigid line inhomogeneity are derived. The project supported by the National Natural Science Foundation of China, the State Education Commission Foundation and the Failure Mechanics Lab of SEdC.     

An anti-plane shear problem

We consider an anti-plane shear of an elastic cylinder with a non-convex stored energy function. So, we look for solutions of a non-convex problem of the calculus of variations with Dirichlet boundary conditions. We give sufficient conditions on the boundary data to get existence or non-existence results for this non-convex problem. We also prove some uniqueness results for the relaxed problem associated with the initial problem.     

On finite anti-plane shear for compressible elastic circular tube

Knowles' theorem for anti-plane shear of compressible, homogeneous, isotropic elastic materials in finite elastostatics is used to determine some restrictions on a strain-energy density function characterizing materials for which two anti-plane shear problems of a circular tube are then solved exactly.

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Resumé Le theorème de Knowles pour le cisaillement anti-plane de matériaux compressibles, homogénes, isotropes, élastiques en élastostatique finie est utilisé afin de déterminer certaines restrictions sur un fonction-densité d'énergie de déformation caractérisant des matériaux pour lesquels deux problèmes de cisaillement anti-plan d'un tube circulaire sont alors résolus exactement.

     

A solution for an isotropic sector under anti-plane shear loadings

In this study, the problem of an isotropic sector subjected to anti-plane shear loadings is investigated. The loadings were applied to the arc of the sector, and the radial edges of the sector were under traction-free or fixed conditions. Depending on these conditions, three problems, namely, free–free, fixed–free, and fixed–fixed edges were studied. A procedure using the finite Mellin transform combined with the Laplace transform was proposed for solving these problems. Explicit closed form solutions for the displacement and stress fields throughout the sector were obtained. The stress intensity factor (SIF) for each problem was analyzed using the obtained stress fields. It was determined that the SIF disappeared under the special condition of a fixed–fixed edge. Other special cases having anti-symmetric conditions were deduced from the derived solutions, and the results of these verified those cited in the literature as well as those obtained using finite element analysis (FEA).     

Finite-deformation crack in an infinite body under anti-plane simple shear

The anti-plane shear crack problem in an infinite body is studied within the context of finite-deformation elastostatics. The governing equations are found to be identical to those of certain previously studied small strain plastic problems under anti-plane shear. For a particular strain energy function, an exact solution of the problem is obtained through use of results in the literature.     

On anisotropic compressible materials that can sustain elastodynamic anti-plane shear

We characterize the class of compressible, homogeneous, possibly anisotropic elastic materials that can undergo nontrivial finite elastodynamic anti-plane shear motions.     

Fully plastic crack in an infinite body under anti-plane shear

The problem of a semi-infinite body with an edge crack subjected to far out-of-plane shear is solved by a transformation to a hodograph plane and the Wiener-Hopf technique. The material stress-strain behavior is governed by a pure power hardening relation and the results are valid for both deformation theory and flow theory of plasticity. Results are presented for crack opening displacement, path independent J integral and crack tip singularities for all finite values of the power hardening parameter.     

Nonlinear response of anti-plane shear crack

Investigated in this communication is the nonlinear response of an anti-plane shear crack. A nonlinear hardening/softening relation is assumed between the resultant shear stress and shear strain for determining the state of affairs near the crack tip. Amplification of the local stress fields is obtained in terms of the material parameters by assuming that nonlinearity is confined to the immediate vicinity of the crack tip region.     

The propagation and arrest of an edge crack in anti-plane shear

The motion of an edge crack extending non-uniformly in an elastic half-space under conditions of anti-plane shear is investigated, taking the first reflected stress wave into account. An expression for the stress intensity factor at the crack tip is obtained, and an energy-balance crack propagation criterion is used to find the equation of motion of the tip. On solving this equation numerically, it is found that crack arrest occurs before the second reflected wave reaches the tip.     

Consequences of the Maxwell relation for anti-plane shear deformations of an elastic solid

Previous numerical work has predicted chaotic distributions of phases in certain deformations of an elastic solid whose stress-strain relation in simple shear is nonmonotone. The present work provides an interpretation of these results making use of elastic stability considerations. For a specific material, a conformal mapping technique is shown to generate the totality of all deformations satisfying the Maxwell relation. It is shown that some boundary value problems have no solutions which obey the Maxwell relation. Such problems may have associated with them an infinite sequence of deformations (corresponding to a minimizing sequence in variational calculus) which satisfies the Maxwell relation in the sense of a limit. The properties of such sequences are examined in detail, and it is shown that the chaotic numerical solutions may be interpreted as terms in this sequence.     

On Saint-Venant's principle in finite anti-plane shear: An energy approach

Dedicated to Bernard Coleman on the occasion of his 60^th birthday     

Stress and electric fields in an infinite electrostrictive plate with an elliptic inhomogeneity

The stress and electric fields in electrostrictive materials under general electric loading at infinity are obtained in this paper. It is shown that the pseudo total stresses are continuous in the whole body. The elliptic inhomogeneity problem is first discussed in this paper and its solution is also given. The results show that the stress in the inhomogeneity is not uniform which is different from the solution of Eshelby theory for elastic materials. When the inhomogeneity and matrix have the same dielectric permittivity or the matrix is a non-electrostrictive material, the stress field is uniform in the inhomogeneity. The form of stress function is simple when the inhomogeneity degenerates to a circle.     

Fully plastic center-cracked strip under anti-plane shear

The problem of a center-cracked strip subjected to uniform remote anti-plane shear stress is transformed to a problem in a hodograph plane which is solved exactly by Mellin transform and Wiener-Hopf technique. The material of the strip satisfies a pure power hardening stress strain relation and the results are valid for both deformation and flow theories of placticity. Numerical values are given for the crack opening displacement δ and Rice's path independent J integral for several values of the power hardening exponent n and crack width to strip width ratios. Approximate asymptotic formulas are presented for J and δ for large n.     

Scattering of harmonic anti-plane shear waves by an interface crack in magneto-electro-elastic composites

IntroductionCompositematerialconsistingofapiezoelectricphaseandapiezomagneticphasehasdrawnsignificantinterestinrecentyears,duetotherapiddevelopmentinadaptivematerialsystems .Itshowsaremarkablylargemagnetoelectriccoefficient,thecouplingcoefficientbetweenst…     

Dynamic anti-plane shear of a cracked piezoelectric ceramic

The dynamic theory of antiplane piezoelectricity is applied to solve the problem of a line crack subjected to horizontally polarized shear waves in an arbitrary direction. The problem is formulated by means of integral transforms and reduced to the solution of a Fredholm integral equation of the second kind. The path-independent integral G is extended here to include piezoelectric effects, and is evaluated at the crack tip to obtain the dynamic energy release rate. Numerical calculations are carried out for the dynamic stress intensity factor and energy release rate. The material is piezoelectric ceramic.     

ELECTROELASTIC FIELD FOR AN IMPERMEABLE ANTI-PLANE SHEAR CRACK IN A PIEZOELECTRIC CERAMICS PLATE

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Fatigue crack growth under anti-plane shear mode deformation

In this paper, the theory of the steady growth of fatigue crack in an infinite medium under the periodic anti-plane remote shear loading has been examined. The criterion of accumulative plastic work for material failure associated with the slip displacement in the fracture process zone of Dugdale type ahead of the crack tip is employed in the analysis. The effect of the locked dislocation in the fracture process zone is considered. Under the assumption that the speed of fatigue crack propagation remains uniform through the fracture process zone, the steady speed of fatigue crack can be expressed as a function of the range of the applied shearing stress and the maximum shearing stress. The effect of the crack size on the fatigue crack speed is discussed. The effect of the finite width of specimen on the speed of fatigue crack speed is investigated. The differences between the present work and the previous studies on fatigue crack speed are discussed.     

Electroelastic field for an impermeable anti-plane shear crack in a piezoelectric ceramics plate

Electroelastic behavior of a cracked piezoelectric ceramics plate subjected to four cases of combined mechanical-electrical loads is analyzed. The integral transform method is applied to convert the problem involving an impermeable anti-plane crack to dual integral equations. Solving the resulting equations, the explicit analytic expressions for electroelastic field along the crack line and the intensity factors of relevant quantities near the crack tip and the mechanical strain energy release rate are obtained. The known results for an infinite piezoelectric ceramics plane containing an impermeable anti-plane crack are recovered from the present results only if the thickness of the plate h → ∞. Biography: LI Xian-fang (1964-)